#
#  Turn off paging.
#
$
#
#  Get a brief list of legal commands.
#
h
#
#  Get the full list of legal commands.
#
help
#
#  Work in fractional arithmetic.
#
rational
#
#  Enter a 3 by 3 matrix.
#
e
3,3
1,2,3
4,5,6
7,8,11
#
#  Interchange rows 1 and 3
#
r1 <=> r3
#
#  Divide row 1 by 7
#
r1 <= r1/7
#
#  Add -4 times row 1 to row 2,
#  Add -1 times row 1 to row 3.
#
r2 <= r2 - 4 r1
r3 <= r3 - 1 r1
#
#  Interchange rows 2 and 3
#  and divide row 2 by 6/7.
#
r2 <=> r3
r2 <= r2 / 6/7
#
#  Add -8/7 times row 2 to row 1,
#  Add -3/7 times row 2 to row 3.
#
r1 <= r1 - 8/7 r2
r3 <= r3 - 3/7 r2
#
#  Check for row reduced echelon form.
#
check
#
#  Divide row 3 by -1
#
r3 <= - r3
#
#  Add 1/3 row 3 to row 1
#  Add -5/3 row 3 to row 2
#
r1 <= r1 + 1/3 r3
r2 <= r2 -5/3 r3
#
#  Consider another matrix
#
e
3,3
1,2,3
4,5,6
7,8,9
#
#  Request automatic conversion to row reduced echelon form.
#
z 31984
#
#  Restore the original matrix.
#
restore
#
#  Insert a new row at row position 3.
#
g +r3
6.1, 6.2, 6.3
#
#  Change entry 3,2 to 77
#
a(3,2) = 77
#
#  Remove column 2.
#
g -c2
#
#  Get a determinant test matrix of order 4.
#
b d 4
det
#
#  Repeat work in real arithmetic.
#
real
e
3,3
1,2,3
4,5,6
7,8,11
#
r1 <=> r3
r1 <= r1/7
r2 <= r2 -4 r1
r3 <= r3 - r1

r2 <=> r3
r2 <= r2 / 0.8571428
r3 <= r3 - 0.4285712 r2
 
r3 <= r3 / -0.9999996
#
check
#
#  OK, cheat and force the entry to be zero.
#
a(3,2) = 0.0
check
#
e
3,3
1,2,3
4,5,6
7,8,9
z
#
r
#
#  Insert a row.
#
g +r3
6.1, 6.2, 6.3
#
#  Change A(3,2) to 77.
#
a(3,2) = 77
#
#  Delete column 2.
#
g -c2
#
#  Get a determinant test matrix of order 4.
#
b d 4
det
#
#  Repeat work in decimal arithmetic.
#
#
#  Set number of decimal digits to 5
#
dec_digit 5
#
#  Change to decimal arithmetic.
#
decimal
#
#  Enter the test matrix.
#
e
3,3
1,2,3
4,5,6
7,8,11
r1 <= r3
r1 <= r1/7
r2 <= r2 - 4 r1
r3 <= r3 - r1

r2 <=> r3
r2 <= r2 / 0.8571
r3 <= r3 - 0.4284 r2
 
r3 <= r3 / -0.99965
 
#
check
#
#  Enter a new matrix.
#
e
3,3
1,2,3
4,5,6
7,8,9
#
#  Automatically process it.
#
z
#
#  Restore the original matrix.
#
r
#
#  Insert a row.
#
g +r3
6.1, 6.2, 6.3
#
#  Change entry (3,2) to 77.
#
a(3,2) = 77
#
#  Remove column 2.
#
g -c2
#
#  Get a determinant test matrix of order 4.
#
b d 4
det
#
#  Work in real arithmetic
#
real
#
#  Get a sample matrix for the Jacobi method.
#
b e 4
#
#  Use Jacobi rotations.
#
j 1,2
3,2
4,2
4,3
3,2
4,2
4,3
3,2
q
#
#  Switch to Linear Programming mode, 
#  and don't save the current matrix.
#
l
no
#
#  Get a brief list of linear programming commands.
#
h
#
#  Work in fractional arithmetic
#
rational
#
#  Get the "simple" linear programming example.
#
b s
#
#  Pivot on the first variable and second row.
#
p 1,2
#
#  Pivot on the second variable, first row.
#
p 2,1
#
#  Check for optimality.
#
check
#
#  Repeat work in real arithmetic
#
real
#
#  Get the "simple" linear programming example.
#
b s
p 1,2
p 2,1
check
#
#  Repeat work in decimal arithmetic
#
decimal
#
#  Get the "simple" linear programming example.
#
b s
p 1,2
p 2,1
check
#
#  Work in fractional arithmetic
#
rational
#
#  Get the "advanced" linear programming example.
#
b a 
#
#  Automatically handle it.
#
z
#
#  Remove artificial variables.
#
v
#
#  Eliminate the nonzero objective row entries associated with
#  the basic variables, X1 and X2.
#
r5 <= r5 + 40 r2
r5 <= r5 + 30 r1
#
#  Reapply the simplex method to the new tableau.
#
z
#
#  Repeat work in real arithmetic
#
real
#
b a 
z
v
r5 <= r5 + 40 r2
r5 <= r5 + 30 r1
z
#
#  Repeat work in decimal arithmetic
#
decimal
#
#  Get the advanced linear programming example.
#
b a
z
v
r5 <= r5 + 40 r2
r5 <= r5 + 30 r1
z
#
#  Quit
#
quit